what is the smallest and greatest 5 digit number divisible by 16,18,24,30?

Question

what is the smallest and greatest 5 digit number divisible by 16,18,24,30

Answer 1

With any group of numbers....

First, find their least common multiple.

1. Break them down to their prime factors.

16 = 2 x 2 x 2 x 2

18 = 2 x 3 x 3

24 = 2 x 2 x 2 x 3

30 = 2 x 3 x 5


Count the maximum number of repetitions for each prime.

for 2, in 16 there are 4 repetitions

for 3, in 18 there are 2 repetitions

for 5, in 30 there is 1 repetition


So the smallest number divisible by all four numbers is

2 x 2 x 2 x 2 x 3 x 3 x 5

16 x 45 = 720.

To see how that works, get your calculator and divide 720 by each of your four numbers.

See it?

Now...

To find 5-digit numbers that can be divided by all 4 numbers, find multiples of 720 that come out to 5 digits.

720 x 2 = 1440
720 x 3 = 2160
720 x ........ go get your calculator and start multiplying!

Answer 2

16=2*2*2*2
18=2* 3*3
24=2*2*2*3
30=2* 3 *5

Ans:2*2*2*2*3*3*5=720 this is the smallest

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